Persistence Criteria for the Nonlocal Niche Model and Applications

Long range dispersal is a common phenomenon in biology and ecology. To have a better understanding of the evolution of biodiversity in some ecosystem, there is a need to understand the influence of nonlocal dispersals on the survival/persistence of a population. In this talk, Xie will report on a recent study concerning persistence criteria in some nonlocal models on temporal and spatial heterogeneous environment. She will present some spectral theory of the associated eigenvalue problem, such as the existence of the principal eigenvalue, and the asymptotic behaviors of the generalized principal eigenvalue with respect to its underlying parameters. As a consequence, she will discuss the applications of these results to the evolutionary invasion analysis. Secondly, the speaker will show some results of the eigenvalue problem with indefinite weight functions, which have practical importance in the context of reserve design or pest control.